Paper ¡ Jun 22, 2016

On Supersymmetric Geometric Flows and Inflation From Scale Invariant Supergravity

Subhash Rajpoot, Sergiu I. Vacaru

hep-tharXiv:1606.06884v3
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As on arXiv

Abstract

Models of geometric flows pertaining to scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic to the Kählerian spaces as generalizations of the non-supersymmetric analogs with manifolds. For curved superspaces with geometric evolution of physical objects, a complete supersymmetric theory has to be elaborated on nonholonomic (super) manifolds and bundles determined by non-integrable superdistributions with additional constraints on (super) field dynamics and geometric evolution equations. We also consider generalizations of Perelman's functionals using such nonholonomic variables which result in the decoupling of geometric flow equations and Ricci soliton equations with supergravity modifications of the gravity theory. As such, it is possible to construct exact non-homogeneous and locally anisotropic cosmological solutions for various types of (super) gravity theories modelled as modified Ricci soliton configurations. Such solutions are defined by employing the general ansatz encompassing coefficients of generic off-diagonal metrics and generalized connections that depend generically on all spacetime coordinates. We consider nonholonomic constraints resulting in diagonal homogeneous configurations encoding contributions from possible nonlinear parametric geometric evolution scenarios, off-diagonal interactions and anisotropic polarization/ modification of physical constants. We also analyze the conditions under which such modified mimetic type theories and solutions reproduce the Starobinsky inflationary models in the double scalar approach.

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Submitted
Jun 22, 2016
Last revised
Jun 28, 2017 (v3)
Subjects
hep-th, math-ph
Journal
Annals of Physics NY 384 (2017) 20-60
DOI
10.1016/j.aop.2017.06.016

Comments: v3 is accepted to AP NY, updated affiliation, and new references; Authors comments on "text overlap with arXiv:1409.7076 ...": together with [T. Gheorghiu et al. AP NY 369 (2016) 1], we present further developments of the published version of arXiv: 1409.7076 - cited several times, with repeating text and results by A. Kehagias, et al

Ricci solitonsPerelman entropyKähler geometryHomogeneous spacesPhysics

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in R² and Einstein Gravity Theories (Tamara Gheorghiu, Vyacheslav Ruchin, Olivia Vacaru et al., 2016)1Gheorghiu 2016 Classical and quantum geometric information flows and entanglement of relativistic mechanical systems (Sergiu I. Vacaru and Laurenţiu Bubuianu, 2019)6Vacaru 2019 Geometric flows and the Swampland (Davide De Biasio, 2023)7De Biasio 2023 Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity (Laurenţiu Bubuianu, Douglas Singleton, Sergiu I. Vacaru et al., 2024)8Bubuianu 2024 Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and F(R,T,Q,Tₘ) gravity (Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev et al., 2024)5Bubuianu 2024 Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics (L. Bubuianu, J. O. Seti, S. Vacaru et al., 2024)3Bubuianu 2024 Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in f(Q) cosmology (L. Bubuianu, E. Nurlan, J. O. Seti et al., 2024)4Bubuianu 2024 The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory (Sergiu I. Vacaru and Elşen V. Veliev, 2025)2Vacaru 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in and Einstein Gravity Theories

    Tamara Gheorghiu, Vyacheslav Ruchin, Olivia Vacaru et al.

    Topics Perelman entropy, Physics, Ricci solitons · Same author Sergiu I. Vacaru · Shared terms “gravity theories”, “geometric flows”, “diagonal”

  2. The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory

    Sergiu I. Vacaru and Elşen V. Veliev

    Topics Perelman entropy, Physics · Same author Sergiu I. Vacaru · Shared terms “gravity theories”, “diagonal”, “locally anisotropic”

  3. Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics

    L. Bubuianu, J. O. Seti, S. Vacaru et al.

    Topics Perelman entropy, Physics, Homogeneous spaces · Same author Sergiu I. Vacaru · Shared terms “geometric flows”, “gravity theories”, “evolution scenarios”

  4. Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in cosmology

    L. Bubuianu, E. Nurlan, J. O. Seti et al.

    Topics Perelman entropy, Physics, Ricci solitons · Same author Sergiu I. Vacaru · Shared terms “geometric flows”, “locally anisotropic”, “diagonal”

  5. Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and gravity

    Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev et al.

    Topics Physics · Same author Sergiu I. Vacaru · Shared terms “diagonal”, “gravity theories”, “configurations”

  6. Classical and quantum geometric information flows and entanglement of relativistic mechanical systems

    Sergiu I. Vacaru and LaurenĹŁiu Bubuianu

    Topics Perelman entropy · Same author Sergiu I. Vacaru · Shared terms “geometric flows”, “modelled”

  7. Geometric flows and the Swampland

    Davide De Biasio

    Topics Perelman entropy, Physics · Shared terms “geometric flows”, “supersymmetric”, “reproduce”

  8. Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity

    LaurenĹŁiu Bubuianu, Douglas Singleton, Sergiu I. Vacaru et al.

    Topics Physics · Same author Sergiu I. Vacaru · Shared terms “gravity theories”, “nonholonomic”, “geometric flows”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Perelman entropy Perelman found that Ricci flow is a gradient flow once a measure is fixed. His 𝓕-functional and 𝓦-entropy increase along the flow; a lower bound… Start with: The entropy formula for the Ricci flow and its geometric applications (Perelman, 2002) Kähler geometry Complex manifolds with compatible Riemannian metrics whose Kähler form is closed. Here Ricci curvature is the complex Hessian of a log-determinant… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978) Homogeneous spaces On homogeneous spaces Ricci flow reduces to an ordinary differential equation on a finite-dimensional space of invariant metrics. Start with: Ricci flow of locally homogeneous geometries on closed manifolds (Isenberg et al., 1992)

In the guidebook

  1. 6A.12
    Entropy, Information and DiffusionBook 6A ¡ The Heat Equation and Its Relatives

    Entropy along the heat flow, the log-Sobolev inequality and Li–Yau: the ancestors of Perelman’s entropy.

  2. 6A.13
    Self-Similar Variables and MonotonicityBook 6A ¡ The Heat Equation and Its Relatives

    Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.

  3. 6B.16
    Eigenvalue Problems and Perelman’s λBook 6B · Linear PDE: Characteristics, Waves and Regularity

    Rayleigh quotients and min–max, Faber–Krahn and Cheeger’s inequality, ground states of Schrödinger operators, spectral clustering, and the first eigenvalue of −4Δ + R that begins Perelman’s first preprint.